A new inverse planning formalism with explicit DVH constraints and kurtosis-based dosimetric criteria

In inverse planning processes of radiotherapy, dose-volume histograms (DVH) have been commonly used as a measure of plan quality. The exact mathematical formulation of DVHs involves binary variables and is therefore intrinsically nonconvex. In view of the resulting computational intractability, existing treatment planning systems adopt convex surrogate models that involve many parameters. Manual parameter tweaking is then required to determine reasonable values for those parameters in order to generate plans that meet the target DVHs. However, conventional convex formulations for inverse planning entails non-trivial differences from an exact formulation and, therefore, provide only very limited control over the DVHs. In view of this limitation, this paper presents a new formulation that combines a novel folded concave penalty (FCP)-based constraint and a new kurtosis-based optimization criterion. The former presents a much sharper approximation to the exact DVH constraints than the existing counterparts, and the latter penalizes the occurrence of hot and cold spots in dose distributions. We investigated the effectiveness of the proposed planning formulations on three head-and-neck cases in comparison with conventional DVH-based formulations. Significant outperformance in terms of better distributed doses-at-volume was achieved through the proposed scheme.